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Quantized Einstein Metrics on $S^7$ with $SU(3)$-Symmetry
We prove that the standard cohomogeneity-one action of \(SU(3)\) on \(S^7\), with principal orbit the Wallach flag manifold \(SU(3)/T^2\), admits infinitely many invariant Einstein metrics. The proof uses a detection approach to the Einstein boundary-value problem. Starting from one singular orbit
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